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arXiv · 1612.07407

Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules

Mauricio Gabriel Medina Bárcenas·Lorena Morales Callejas·Martha Lizbeth Shaid Sandoval Miranda·Angel Zaldívar
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Abstract

In this paper we study some frames associated to an $R$-module $M$. We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of $Max(M)$. We characterize the soberness of $Max(M)$ in terms of the point space of that frame. Beside of this, we study the regularity of an spatial frame associated to $M$ given by annihilator conditions.

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Mauricio Gabriel Medina Bárcenas, Lorena Morales Callejas, Martha Lizbeth Shaid Sandoval Miranda, Angel Zaldívar. 2016-12-22. Attaching topological spaces to a module (I): Sobriety and spatial frames of submodules. https://arxiv.org/abs/1612.07407

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